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New posts: _posts/2024-08-01-Useful-Mathematica-functions-for-signal-processing-units.md

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---
title: Useful Mathematica functions for signal processing units
author: peter
date: 2024-08-01 01:40:23 +0800
categories: [Uni] # Blogging | Electronics | Programming | Mechanical | SelfHosting
tags: [ELEC4402] # systems | embedded | rf | microwave | electronics | solidworks | automation | tip
# image: assets/img/2024-08-01-Useful-Mathematica-f/preview.png
---
I will update this as I add more functions.
Using it for the unit ELEC4402 Communication Systems
```mathematica
(* Signal power *)
SigPower[expr_, t_] :=
Limit[1/(2 T) Integrate[expr, {t, -T, T}], T -> Infinity]
(* Normalized sinc function, default Sinc in Mathematica is not normalized *)
SincNorm[Infinity] := Sinc[Pi Infinity]
SincNorm[t_?NumericQ] := Sinc[Pi t]
(* Fourier transform, frequency in Hz *)
FTfreq[varargs__] :=
FourierTransform[varargs,
FourierParameters -> {0, -2*Pi}] /. {Sinc[f_] :>
SincNorm[Simplify[f/Pi]]}
(* Inverse Fourier transform, frequency in Hz *)
IFTfreq[varargs__] :=
InverseFourierTransform[varargs,
FourierParameters -> {0, -2*Pi}] /. {Sinc[f_] :>
SincNorm[Simplify[f/Pi]]}
```